On Stable Solutions of the Fractional Henon-lane-emden Equation
نویسندگان
چکیده
We derive a monotonicity formula for solutions of the fractional Hénon-Lane-Emden equation (−∆)u = |x|a|u|p−1u R where 0 < s < 2, a > 0 and p > 1. Then we apply this formula to classify stable solutions of the above equation.
منابع مشابه
New Solutions for Singular Lane-Emden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives
In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the eq...
متن کاملNumerical Solution of the Lane-Emden Equation Based on DE Transformation via Sinc Collocation Method
In this paper, numerical solution of general Lane-Emden equation via collocation method based on Double Exponential DE transformation is considered. The method converts equation to the nonlinear Volterra integral equation. Numerical examples show the accuracy of the method. Also, some remarks with respect to run-time, computational cost and implementation are discussed.
متن کاملOn the Fractional Lane-emden Equation
We classify solutions of finite Morse index of the fractional LaneEmden equation (−∆)su = |u|p−1u in R.
متن کاملA Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane–-Emden Type Equations
In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...
متن کاملOn Finite Morse Index Solutions of Higher Order Fractional Lane-emden Equations
We classify finite Morse index solutions of the following nonlocal Lane-Emden equation (−∆)u = |u|p−1u R for 1 < s < 2 via a novel monotonicity formula. For local cases s = 1 and s = 2 this classification is provided by Farina in [10] and Davila, Dupaigne, Wang and Wei in [8], respectively. Moreover, for the nonlocal case 0 < s < 1 finite Morse index solutions are classified by Davila, Dupaigne...
متن کامل